Does WordPress refer to any files outside of the main install folder (and database)?

The short answer is no, WordPress does not refer to any files outside of the main install folder.
When WordPress loads (via /wp-load.php), it sets the constant ABSPATH to the current directory path and points all further includes relative to that.

However, since you are asking, there are some notable special cases:

• If you install WP in its own directory, you have to copy the index.php and .htaccess file outside the WP directory to the parent directory.
• WordPress checks if wp-config.php exists in its parent directory so you could also have that one outside of the main directory.
• The wp-content, plugins, uploads and theme directory can be moved to pretty much anywhere.

These are all options and not default behavior. So the answer remains no.